Dr Rice, who left office in 2009, is currently a professor of political science at Stanford University in California. Getty Images

Republican presidential hopeful Donald Trump reportedly called former secretary of state Condoleezza Rice over the weekend to see if she was interested in being his running mate - an offer she promptly turned down.

Sources told CNN reporters Dana Bash and Elise LaBott that before naming Indiana Governor Mike Pence as his running mate, the billionaire real estate developer had "reached out to Condi Rice in [the] last few days," but Rice "had no interest" in the role.

Rice, who left office in 2009 after serving as National Security Adviser and later as Secretary of State in the George W Bush administration, is presently a political science professor at Stanford University in California.

Her spokesman said last month that she was "not interested in being vice president," adding: "She's happy at Stanford and plans to stay."

The Independent notes that adding a black woman to the ticket "would have been a coup for Mr Trump," as he is polling at zero per cent among black voters in the key swing states of Pennsylvania and Ohio, according to two new NBC/Wall Street Journal polls.

Rice would have boosted Trump's popularity among Evangelical voters as well. After her stirring prayer at Menlo Park Presbyterian Church in which she urged the U.S. to "race toward God" amid the recent spat of violence seen across the nation, Rice garnered high praise from many in the faith-based community, including influential evangelist Franklin Graham.

"She would make a great President one day! God bless her unashamed stand for the Lord Jesus!" wrote one online supporter.

"Boy would she be an excellent VP," wrote another.

"This is what America is craving right now...those who will speak truth, honesty with humility and offer healing to our people," added another.

Meanwhile, just days before the kickoff of the Republican National Convention, Trump named Pence as his running mate, a Republican who previously served in the U.S. House of Representatives and sometimes describes himself as "a Christian, a conservative and a Republican, in that order."

According to Time Magazine, Trump made the decision after days of consulting with a number of Christian leaders, including Liberty University president Jerry Falwell, televangelist James Robison, and Graham.

"Pence seemed to bring understanding of working in the arena new to Trump and important balance to Trump, and would build confidence in his own judgment and recognition of the importance of wise counsel," Robison said. "I had made it clear God uses imperfect people to accomplish his perfect will....when the imperfect hear and heed wise counsel."